The beginning to any story comes with two implied circumstances: this is not the real beginning, nor is it the real end.
Any fairy tale comes with a back story that unfolds as the account progresses. Every character has already begun to walk the path that leads them to their conflict. They've already been through experiences that have shaped them into the protagonist.
Once upon a time is just that: the story happened once, a long time ago. The repercussions of its events have already begun to take effect. Happily ever after isn't the real ending; the bigger picture just hasn't been unveiled yet.
Now let's suppose I'm a character in a fairy tale. Like any other fairy tale, you don't know my back story. You haven't yet been told my name, my character, my mysteries, my life. You have only been given the circumstances that come with any other story: this is neither the beginning, nor is it truly "over."
Once upon a time, there was a girl named Lizzie.